Match List-I with List-II and select the correct answer: List-I List-II a. Coefficient of determination 1. $${\gamma _{xy}}\frac{{{\sigma _x}}}{{{\sigma _y}}}$$ b. Spearman’s rank correlation coefficient 2. $$1 – \frac{{6\sum {{d^2}} }}{{n\left( {{n^2} – 1} \right)}}$$ c. Regression coefficient of $$x$$ on $$y$$ variable 3. $$\frac{{\sum {xy} }}{{n\,{\sigma _x}\,{\sigma _y}}}$$ d. Karl Pearson’s formula of calculating $$\gamma $$ 4. $${\gamma ^2}$$

The correct answer is: A. a-1, b-4, c-2, d-3

Here is a brief explanation of each option:

• Coefficient of determination is a measure of how well the data fits a straight line. It is calculated by taking the square of the correlation coefficient.
• Spearman’s rank correlation coefficient is a measure of the correlation between two variables, where the variables have been ranked. It is calculated by taking the sum of the products of the ranks of the two variables, and dividing by the number of pairs of observations.
• Regression coefficient of $x$ on $y$ variable is a measure of the strength of the linear relationship between $x$ and $y$. It is calculated by taking the slope of the line of best fit.
• Karl Pearson’s formula of calculating $\gamma$ is a formula for calculating the correlation coefficient between two variables. It is calculated by taking the covariance of the two variables, and dividing by the product of their standard deviations.

Here is a table that shows the correct match between List-I and List-II:

| List-I | List-II |
|—|—|
| a. Coefficient of determination | 1. $${\gamma _{xy}}\frac{{{\sigma _x}}}{{{\sigma _y}}}$$ |
| b. Spearman’s rank correlation coefficient | 4. $${\gamma ^2}$$ |
| c. Regression coefficient of $x$ on $y$ variable | 3. $$\frac{{\sum {xy} }}{{n\,{\sigma _x}\,{\sigma _y}}}$$ |
| d. Karl Pearson’s formula of calculating $\gamma$ | 2. $$1 – \frac{{6\sum {{d^2}} }}{{n\left( {{n^2} – 1} \right)}}$$ |